Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures

TL;DR

This paper numerically studies edge states in fractional quantum Hall-superconductor heterostructures, revealing topological properties and fractional Josephson effects that could enable quantum information applications.

Contribution

It introduces a numerical approach to analyze gapped edge states in fractional quantum Hall-superconductor systems, demonstrating their topological features and quasiparticle pairing.

Findings

Edge ground states are permuted by spin-dependent flux insertion.

The system exhibits a fractional 6π Josephson effect.

Topological protection of quantum information in the edge states.

Abstract

Fractional quantum Hall-superconductor heterostructures may provide a platform towards non-abelian topological modes beyond Majoranas. However their quantitative theoretical study remains extremely challenging. We propose and implement a numerical setup for studying edge states of fractional quantum Hall droplets with a superconducting instability. The fully gapped edges carry a topological degree of freedom that can encode quantum information protected against local perturbations. We simulate such a system numerically using exact diagonalization by restricting the calculation to the quasihole-subspace of a (time-reversal symmetric) bilayer fractional quantum Hall system of Laughlin $\nu=1/3$ states. We show that the edge ground states are permuted by spin-dependent flux insertion and demonstrate their fractional $6\pi$ Josephson effect, evidencing their topological nature and the Cooper pairing of fractionalized quasiparticles.